▎ 摘　　要

Graphene is considered an ideal material candidate in the design and manufacturing of flexible electronics and devices because of its ultrahigh out-of-plane mechanical flexibility along with high thermal conductivity. However, the associated thermal management is vulnerable to mechanical deformation and the thermal transport of graphene/substrate systems subjected to mechanical bending deformation remains fundamentally unclear. Here, we investigate the thermal transport of mechanically bent graphene on a flexible substrate using non-equilibrium molecular dynamics (NEMD) simulations. We find that the thermal conductivity shows an anomalous nonlinear decrease with the increase of bending curvature for a small-sized graphene/substrate and becomes nearly independent of bending curvature at a large-sized graphene/substrate. A two-phonon model is proposed to quantitatively correlate the thermal conductivity with bending curvature and graphene size, and the predictions are in great agreement with simulations. We further elucidate the underlying mechanism of phonon transport coupled with graphene size and bending curvature by systematically studying the phonon population difference, phonon spectral energy density, and spectral decomposed thermal conductance of graphene/substrate systems. This work uncovers a fundamental mechanism of mechanical and thermal coupling and correlation in graphene/substrate systems for their enabled applications in flexible electronics and also offers guidance in the thermal management of graphene-based flexible devices undergoing severe mechanical deformation.